#10

Mgmt 380

Assignment #4

DUE: Friday, March 3

20 points

The Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of hours of carpentry work and a certain number of labor hours in the painting and varnishing department. Each table takes 4 hours of carpentry and 2 hours in painting and varnishing. Each chair requires 3 hours in carpentry and 1 hour in painting and varnishing. During the current production period, 240 hours of carpentry time are available and 100 hours of painting and varnishing time are available. Each table yields a profit of \$7; each chair produced yields \$5 profit.

Flair’s wants to determine the best possible combination of tables and chairs to manufacture in order to reach the maximum profit. The firm would like this production mix situation formulated as a linear programming model and solved with both a graphical model and the simplex model.

Step 1: Define the problem.

What is the goal? What is the research question? What are the decision variables? What is the objective function? What are the constraints?

Step 2: Gather the data for the problem. (This has been provided.)

Step 3: Build one or more model(s).

In this case, you will build three:

1) mathematical (linear programming) model

2) graphical model

3) simplex model

Submit the following, stapled in order:

1) cover page with your name, course, assignment number, and signature

2) the problem definition (step 1 above)

3) the mathematical (linear programming) model

4) the graphical model:

• Shade the feasible region.
• Circle the possible optimal solutions
• Record the optimal solution.

5) the simplex model:

• Include each tableau iteration; label each one. Note the pivot row, pivot column, and pivot number in each (except the last, optimal one, of course).
• Record the optimal solution.

Keep in mind: The optimal solution acquired with the graphical method and the optimal solution acquired with the simplex method should obviously be the same. And, if Flair asked you to also do a spreadsheet model, it too would result in the same optimal solution as the graphical and simplex model. (But aren’t you glad Flair did not ask you to do this?)

Note: As with all assignments, this one must be presented in a professional manner, typed, spell-checked, and grammar-checked.

The following blank tableau is provided so that you can avoid drawing this table for each iteration. It can be copied.

Simplex Tableau for this Model

Iteration # ___________

 Cj Basic Variables Quantity (RHS) Zj Cj - Zj